Adam, Sam, and Eddie have to meet their boss at 3:00 in the office 9 miles apart from their home, and they must be arrive in time for the appointment. Adam had a bicycle, Sam had a skateboard,and Harry had no transport. So they have to share.
so they left the house together.
Each of them travel on walk at 6 m.p.h.; each of them skateboard at 10 m.p.h.; and each of them cycle at 16 m.p.h.They arrived in time for their 3:00 appointment. At what time did they leave the house?
To determine the time they left the house, we need to calculate the time it takes for each person to travel 9 miles.
First, let's calculate the time taken by Adam on a bicycle.
Adam travels at 16 mph, so the time taken by Adam on a bicycle is given by:
Time taken = Distance / Speed = 9 miles / 16 mph
Next, let's calculate the time taken by Sam on a skateboard.
Sam travels at 10 mph, so the time taken by Sam on a skateboard is given by:
Time taken = Distance / Speed = 9 miles / 10 mph
Lastly, let's calculate the time taken by Eddie on foot.
Eddie travels at 6 mph, so the time taken by Eddie on foot is given by:
Time taken = Distance / Speed = 9 miles / 6 mph
We know that they arrived on time for their 3:00 appointment, which means the total time they took to travel must be less than 3 hours.
Let X be the time taken by Adam, Y be the time taken by Sam, and Z be the time taken by Eddie to reach the office.
Given:
X = 9 miles / 16 mph
Y = 9 miles / 10 mph
Z = 9 miles / 6 mph
To find the time they left the house, we need to find the maximum value of X, Y, and Z.
Comparing the values, we have:
X < Y < Z
Since all the times must be less than 3 hours (or 180 minutes) and the total time cannot exceed 3 hours for them to arrive on time, let's test the values for X, Y, and Z.
First, let's calculate the time taken by Adam:
X = 9 miles / 16 mph = 0.5625 hours * 60 minutes = 33.75 minutes
Next, let's calculate the time taken by Sam:
Y = 9 miles / 10 mph = 0.9 hours * 60 minutes = 54 minutes
Lastly, let's calculate the time taken by Eddie:
Z = 9 miles / 6 mph = 1.5 hours * 60 minutes = 90 minutes
As we see, Eddie's time is the largest, which is 90 minutes.
So, they left the house 90 minutes before their appointment at 3:00 PM.
To calculate the actual departure time, subtract 90 minutes from 3:00 PM:
3:00 PM - 90 minutes = 1:30 PM.
Therefore, they left the house at 1:30 PM.